CGTLife Points Values

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    Keywords: Theory

KarlKnechtel: On SL we have already seen the application of combinatorial game theory to several aspects of Go, mostly to do with raw point counts (see temperature, numbers, infinitesimals and so on... or just go check out the entire CGT path). CGT also applies to eyespace values; and recently, an effort has been made to assign CGT values of connections.

I think this gives us the necessary ingredients to try out CGT techniques in evaluating overall gameplay. Normally CGT is only applied to the study of "local games" (i.e. it is really only relevant in yose), but I am suggesting, basically, that we use the CGT connection evaluation to account for coupling effect.

This is a rough sketch of the algorithm I have in mind, for an evaluation function for one player's stones:

We evaluate the total connection value between two nodes as the sum over all paths between the nodes, of the products of values along those paths.

This is the real tricky part: This is going to be, at worst, O(2^(m^2)) for m strings, the way I've described it. Some simplifications are definitely needed.

Once we have that, we are using WholeBoardConnectionTheory; we can (I think) write programs with a sense of WholeBoardThinking, and apply the usual minimax business. We can consider the 'net score' as (black whole board value - white whole board value), and use minimax to select the move which yields the best improvement in board evaluation. Of course, we still need to prune the tree, and make the evaluation fast. This is way more complex than brute-forcing chess... :)


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